It is important to determine the capillary pressure of porous materials that are used in many applications such as writing instrument reservoirs, mono-clonal antibody based diagnostic test kits, filtration of immiscible fluids or gases with liquid dispersions and other applications that rely on porous materials for the transfer, absorption or release of liquids. In such applications, knowledge of the "pore" size distribution is not sufficient and often, is not very useful. The most common method for measuring the pore size distribution is mercury porosimetry (cf., Adamson, Wiley Interscience, N.Y. 1976), which relies on the measurement of intrusion of a non-wetting fluid, such as mercury Hg, into a test sample at increasing steps of applied pressure. There are many embellishments to the basic method. For example, Determining Saturation And Permeability Using Mercury Capillary Pressure Curves by Yuan et al. (U.S. Pat. No. 4,625,544) measures the response to a slow application of pressure against the mercury capillary pressure to learn more about the detail structure of the sample morphology. Still another variation is Method For Measuring Wettability Of Porous Rock by Sprunt et al. (U.S. Pat. No. 5,069,065) which displaces a first wetting fluid by a second non-wetting fluid that is immiscible with the first wetting fluid.
Yuan et al. '544 and Sprunt et al. '065 do not provide any information regarding the capillary pressure distribution of porous materials using a wetting fluid. The capillary pressure curves referred to in Yuan et al. '544 and Sprunt et al. '065 are simply mercury intrusion volume versus pressure curves. I have observed that these capillary pressure curves do not directly provide any information regarding the fractional area or volume based capillary pressure distribution of the porous material, as contemplated by the present invention. Prior methods calculate the pore size based on an assumption that the sample has a plurality of cylindrical and unconnected pores. The pore size distribution can be determined from the mercury Hg intrusion pressure-volume data as shown (cf. Adamson, Wiley Interscience, N.Y. 1976) in the following expression: EQU D(r)=(P/r)dV/dP, (1)
where D(r) is the pore radius based distribution function, P is the applied pressure, V is the volume of the mercury Hg injected and r is the "pore" radius. It has been my observation that such assumptions are not generally valid, because the cross sections of the pores are varied, with expansions and contractions, and the pores themselves are often interconnected. Furthermore, as the porosity, defined as the void fraction, increases above approximately 0.7, the concept of "pores" breaks down and the applicability of the above equation (1) is doubtful.
In wetted fluid applications, the knowledge of the advancing and receding capillary pressure distribution with respect to the sample average cross section area or volume of the sample is required. This information is necessary for the design and development of liquid absorbency and release products. Advancing (of the liquid interface) and receding pressure curves exhibit hysteresis due to: a) non-uniformity of "pore" cross sections, b) existence of ink wells or dead ends, and c) differences in advancing and receding contact angle. Knowledge of either or both advancing and receding wetted fluid-sample capillary pressure distributions is important in the above applications depending on whether the porous sample is used for absorption (e.g., diagnostic test kits) or for absorption and liquid release (e.g., pen reservoirs). Mercury Hg porosimetry methods differ from the present invention in that only the pore size distribution is determined, using a non-wetting fluid, and that pressure must be applied in order for the non-wetting fluid to penetrate the porous sample, noting that in the above-mentioned wetted fluid applications of porous materials, the wetting fluid penetrate the sample without application of pressure.
There are other methods for measuring pore size distribution of porous samples that do not rely on Hg porosimetry. For example, Pore Determination Of A Porous Member by Roy (U.S. Pat. No. 3,524,341) determines the pore size distribution based on the change of conductivity of a previously saturated (with KCl) porous sample with respect to the displacement of the KCl by a pressurized gas. This results in the calculation of pore size distribution based on the receding flow of the KCl. Roy '341 does not present any method for calculating the sample cross-section area or volume based advancing or receding pore size distribution as determined by the present invention. Additionally, Measurement Of Pore Size And Porosity by Roy (U.S. Pat. No. 3,683,674) discloses a method that uses centrifugal force to release the saturated wetting fluid from the saturated porous sample. Once again, this method determines only the pore size distribution based on receding data. Roy '674 does not disclose a method for measuring the advancing interface based "pore" size, or any sample cross-section area, or volume based capillary pressure distribution. Both the Roy's methods in Pore Determination Of A Porous Member '341 and Measurement Of Pore Size And Porosity '674 utilize the receding displacement volume data for a wetting fluid, and make all the assumptions related to cylindrical pores in order to determine the pore size distribution. Furthermore, they do not determine the capillary pressure distribution of the porous sample.
Lowell, Incremental Method For Surface Area And Pore Size Determination (U.S. Pat. No. 3,555,912), proposes a method for measuring the pore size distribution based on gas absorption of a porous sample, that has been previously degassed. Storr, Porosimeter And Methods Of Assessing Porosity (U.S. Pat. No. 4,718,270), on the other hand, proposes an improvement to a method for determining pore size distribution based on gas flow rate versus pressure of gas that displaces a wetting fluid from a porous sample. I have observed that neither Storr '270 nor Lowell '912 proposes any method for calculating the sample average cross-section area or average volume based capillary pressure distribution. It is important to note that pore size measurements obtained by different physical principals give different results (cf. Adamson 1976). Hence, it is important to use methods that incorporate the same phenomena as the application or use of the porous materials. For example, wetted fluid absorption based measurements are more relevant when the porous material is used as an adsorbent, while mercury Hg displacement methods are more relevant to the displacement of non-wetting materials from a porous sample. The pore size distributions obtained by these different methods are also different. Hence, these methods are not suitable for porous materials used for absorbency and liquid release applications. Moreover, I have also observed that these methods do not measure the advancing and receding capillary pressure distributions of the porous materials; they can only calculate the "pore" size distribution of the porous materials. It is in my opinion that is fundamentally important to note that the prior art methods as disclosed by Yuan, et al. '544, Sprunt, et al. '065, Lowell '912, Storr '270 and Roy '341 and '674 as well as others do not provide for a method of determining the area or volume based advancing and receding capillary pressure distribution of porous materials.